Pose vs Rest position are different
In the Properties panel > Data > Skeleton, display all the layers so that you can see all the bones, now you can check the influence of the different bones, for example the head bone has an influence on the lids so of course the lid bones won't influence them 100%.

Also, if the bones in Pose mode have a different position, it's because they are influenced by some constraints like Copy Rotation or IK. To get exactly the same position as in Edit mode it may need some small bone readjustments.